Consider a perceptron that has two real- valued inputs and an output unit that uses a Sigmoid function as its output function. All the initial weights and the output unit's threshold equal 0.2 Assume that the output should be 0 for the input in1 = 2 and .in2 = 5 Let (the learning rate) be 0.5 %D Show the value of the all weights and the .output after 2 iteration the new weights the output is
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- Profit Suppose that the total weekly cost for theproduction and sale of x bicycles is C(x) = 23x +3420 dollars and that the total revenue is givenby R(x) = 89x dollars, where x is the number ofbicycles.a. Write the equation of the function that models theweekly profit from the production and sale of xbicycles.b. What is the profit on the production and sale of150 bicycles?c. Write the function that gives the average profit perbicycle.d. What is the average profit per bicycle if 150 areproduced and sold?What P(s1) would the decision-maker be indifferent between the "buy" and "make" decisions, all other data input remaining the same?5. Consider the process where S0 = 0 and {ut : t ∈ Z} is an i.i.d. random variable with N(0,σ2). a) DeterminethemeanandcovariancefunctionoftheprocessSt.Isthisprocessstrictlystationary?Second-order stationary? b) Show that the process Yt = (1 − L)St , t = 1,2,... is strictly stationary. Compute its mean and autocovariance function.
- 1. Suppose Firm A has a budget of P1.5 million pesos in outsourcinginputs, labor and machines, that would lend support in its 1 yearoperation. Suppose further that the cost of labor for 1 year is P150,000and for a machine is P200,000. If it decides to hire 6 laborers, howmany machines would it accept?Q. 1 You are the mayor of a small town with 2000 residents. The head of your economic development agency recently conducted a survey in which the 2000 residents said that a public concert in the centre of town would be worth $20 to cach of them. Since it costs only $5000 to hold the concert, you organized and held the concert, which everyone in town enjoyed. But when you asked for donations to pay for the concert, you only collected $30 in total. What do you know? a. The survey certainly overstated how much the concert was worth to each resident. b. From the standpoint of total costs and benefits, the cost of the concert certainly exceceded the benefit. c. The concert was an example of the Tragedy of the Commons. d. Residents of the town were probably free riders.1 Explain what is meant by heteroscedasticity
- The manager of the donut shop tells you that hesells donuts for $1 each, and that if he were to makeadditional donuts, based on his current level ofoutput, it would cost him $0.80 per donut. Do yourecommend that the manager increase or decreasethe number of donuts he makes?s EconomicsQ&A LibraryEach term (3 months) the current group of economics students completed a questionnaire as to how much they would spend on new purchases compared to how much they would save/pay off bills, if they suddenly and unexpectedly received a check for $1,000. The average MPC is shown in the table below. Month in which student poll was taken Average of students’ responses as MPC March 0.41 June 0.30 September 0.22 December 0.56 What do these MPC’s imply about the students’ thinking over the course of the year? (Enter response here.) What is likely happening in the economy during the same period of time? Each term (3 months) the current group of economics students completed a questionnaire as to how much they would spend on new purchases compared to how much they would save/pay off bills, if they suddenly and unexpectedly received a check for $1,000. The average MPC is shown in the table below. Month in which student poll was taken Average of students’…(a) The sales of a book publication are expected to grow according to the functionS = 300000(1 − e−0.06t), where t is the time, given in days.(i) Show using differentiation that the sales never attains an exact maximum value.(ii) What is the limiting value approached by the sales function?(b) A poll commissioned by a politician estimates that t days after he makes a statementdenegrating women,the percentage of his constituency (those who support him at the time hemade the statement) that still supports him is given by S(t) =75(t2 − 3t + 25)t2 + 3t + 25The election is 10 days after he made the statement.(i) If the derivative S’(t) may be thought of as an approval rate, derivate the a functionfor his approval rate.(ii) When was his support at its lowest level?(iii) What was his minimum support level?(iv) Was the approval rate positive or negative on the date of the election?(c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curvefor the bast will be…
- Define Say’s LawSuppose that there is a 20 percent change that George's coffee shop will make $9000 in profits in January and a 40 percent chance it will make 1000 profits and a 40 percent chance that it will make -$1000 in profits (i.e., it will lose $1000). Calculate the coffee shop's expected profitsA farmer believes there is an equal chance that the next growing season will be abnormallyrainy. His expected return function has the formExpected return = 0.5lnYNR + 0.5lnYRwhere YNR and YR represent the farmer’s income in the states of “normal rain”and “rainy,” respectively.Suppose the farmer must choose between two crops that promise the following incomeprospects:Crop YNR YRMaize $14,000 $5,000Cotton $9,500 $7,500a) Which of the crops will he plant?b) Suppose the farmer can plant half his field with each crop. Would he choose to do so?Explain your result.c) What mix of Maize and Cotton would provide maximum expected utility to this farmer?d) Would Maize crop insurance, available to farmers who grow only Maize, which costs$2,000 and pays off $4,000 in the event of a rainy growing season, cause this farmer tochange what he plants?